reduce vs cut down

reduce and cut down both are verbs.

Word	Noun	Adjective	Verb	Adverb
reduce	No	No	Yes	No
cut down	No	No	Yes	No

As verbs, reduce and cut down are synonyms defined as:

Other synonyms of reduce include bring down, cut, cut back, trim, trim back, trim down.

reduce (verb)	cut down (verb)
take off weight	cut down on; make a reduction in
cut down on; make a reduction in	intercept (a player)
narrow or limit	cause to come or go down
cook until very little liquid is left	cut with a blade or mower
to remove oxygen from a compound, or cause to react with hydrogen or form a hydride, or to undergo an increase in the number of electrons	cause to fall by or as if by delivering a blow
make smaller	cut with sweeping strokes; as with an ax or machete
reduce in size; reduce physically
make less complex
reduce in scope while retaining essential elements
lessen the strength or flavor of a solution or mixture
be cooked until very little liquid is left
be the essential element
destress and thus weaken a sound when pronouncing it
undergo meiosis
reposition (a broken bone after surgery) back to its normal site
lower in grade or rank or force somebody into an undignified situation
lessen and make more modest
simplify the form of a mathematical equation of expression by substituting one term for another
bring to humbler or weaker state or condition
put down by force or intimidation